The middle widget area is coded to show to posts/pages side by side and the bottom widget area is coded to show posts/pages one per line. However, there is nothing stopping you from added more than one featured content widget to the middle widget area to achieve multiple categories/sections with two posts/pages side by side. You could leave the bottom widget area empty.

In your WordPress dashboard, under the Genesis menu, click on ‘Theme Settings’. Under the ‘Navigation’ section click the checkbox for “Enable Extras on Right Side” under ‘Primary Navigation’. You will see a drop down which will let you select to display a search form.

You may want to add a background to the search box as it is showing the slider through. Actually a semi-transparent white would look good, or change the text to white and go with a semi-transparent black.

When I increase my browser width, it’s like the logo is pinned to the right side of the screen.

This is not supposed to be like this. I think you missed adding ‘position: relative’ to your .wrap rule. Adding this will fix it.

Now lets look at narrow screen sizes. Your “desktop design” is two columns (content and sidebar) and we’ve set up the CSS to position your logo in the “right column”. When viewing the site on a tablet or mobile phone, your theme reduces to one column. You as the designer/developer need to determine how you want your layout to be on these devices.

One option would be to position the logo top center, with the menu below it, and then the main content. Your theme does this out of the box, but we made some changes last time to get the full-width view the way you want, so we need to add CSS rules to “put things back” at narrower screen sizes.

The StudioPress style sheets group the mobile responsive CSS rules at the bottom. If you open your style sheet and scroll to the bottom you will see settings for various max-widths ie: